A projection on the span of a singleton. (The proof ws shortened by
Mario Carneiro, 15-Dec-2013.) (Contributed by NM, 28-May-2006.)
(Revised by Mario Carneiro, 15-Dec-2013.)
(New usage is discouraged.)

A subset of Hilbert space is orthogonal to the span of the singleton of
a projection onto its orthocomplement. (Contributed by NM,
4-Jun-2004.) (Revised by Mario Carneiro, 15-May-2014.)
(New usage is discouraged.)

Foulis-Holland Theorem. If any 2 pairs in a triple of orthomodular
lattice elements commute, the triple is distributive. First of two
parts. Theorem 5 of [Kalmbach] p. 25.
(Contributed by NM, 14-Jun-2006.)
(New usage is discouraged.)

Foulis-Holland Theorem. If any 2 pairs in a triple of orthomodular
lattice elements commute, the triple is distributive. Second of two
parts. Theorem 5 of [Kalmbach] p. 25.
(Contributed by NM, 14-Jun-2006.)
(New usage is discouraged.)

Foulis-Holland Theorem. If any 2 pairs in a triple of orthomodular
lattice elements commute, the triple is distributive. First of two
parts. Theorem 5 of [Kalmbach] p. 25.
(Contributed by NM,
7-Aug-2004.) (New usage is discouraged.)

Foulis-Holland Theorem. If any 2 pairs in a triple of orthomodular
lattice elements commute, the triple is distributive. Second of two
parts. Theorem 5 of [Kalmbach] p. 25.
(Contributed by NM,
7-Aug-2004.) (New usage is discouraged.)